Magnetic phase diagram, magnetoelastic coupling and Gr\"uneisen scaling in CoTiO$_3$

High-quality single crystals of CoTiO$_3$ are grown and used to elucidate in detail structural and magnetostructural effects by means of high-resolution capacitance dilatometry studies in fields up to 15 T which are complemented by specific heat and magnetization measurements. In addition, we refine the single-crystal structure of the ilmenite ($R\bar{3}$) phase. At the antiferromagnetic ordering temperature $T_\mathrm{N}$, pronounced $\lambda$-shaped anomaly in the thermal expansion coefficients signals shrinking of both the $c$ and $b$ axes, indicating strong magnetoelastic coupling with uniaxial pressure along $c$ yielding six times larger effect on $T_\mathrm{N}$ than the pressure applied in-plane. The hydrostatic pressure dependency derived by means of Gr\"uneisen analysis amounts to $\partial T_\mathrm{N}/ \partial p\approx 2.7(4)$~K/GPa. The high-field magnetization studies in static and pulsed magnetic fields up to 60~T along with high-field thermal expansion measurements facilitate in constructing the complete anisotropic magnetic phase diagram of CoTiO$_3$. While the results confirm the presence of significant magnetodielectric coupling, our data show that magnetism drives the observed structural, dielectric, and magnetic changes both in the short-range ordered regime well-above $T_\mathrm{N}$ as well as in the long-range magnetically ordered phase.